Bulletin of the
Korean Mathematical Society BKMS

Let $T$ be an $m$-linear Calder\'on-Zygmund operator. $T_{\vec{b},S}$ is the generalized commutator of $T$ with a class of measurable functions $\{b_{i}\}_{i=1}^\infty$. In this paper, we will give some new estimates for $T_{\vec{b},S}$ when $\{b_{i}\}_{i=1}^\infty$ belongs to Orlicz-type space and Lipschitz space, respectively.

Keywords: Multilinear operators, weight, generalized commutator, $BMO$ function

MSC numbers: 42B20, 42B25

Supported by: This work was supported by Natural Science Foundation of Henan (No.232300421142; No.202300410184), the Key Research Project for Higher Education in Henan Province (No.19A110017) and the Fundamental Research Funds for the Universities of Henan Province (No.NSFRF200329)..